Evoking the religious and the sublime ... The Weather Project, an installation by Olafur Eliasson in Tate Modern, 2003.

It is not especially original, but it's hard not to notice the striking similarities between theatre and organised religion: the communal experience, the gathering together in one place to bear witness; finding a space within a crowd to reflect in silence on one's thoughts; the civic, social and, to an extent, pastoral needs which both can fulfil. For the ancient Greeks, theatre clearly played an important part in the intellectual and moral life of the city; it's probably reasonable to speculate that the day-long performances of tragedies must have accrued some of the heady atmosphere of the religious trance. But in Shakespeare's deeply sectarian Christian world, while frowned on by protestantism, theatres seemed to distance themselves from overt expressions of religious faith. And so, the raucous, secular, circular space of the Globe offers an almost precise opposite of the hushed, reverent cruciform of a cathedral. From the 17th century onwards, an essential secularity seems to have been established in theatre, both in terms of content and architecture. There are superficial similarities between the narrower proscenium arch theatres and more ornate churches, but such similarities tend not to resonate. If the wings of the stage are the choir, then the altar has been excised; in theatre, at least, the cross has been decapitated.

Yet, in our contemporary world, a certain amount of ecclesiastical atmosphere has been reintroduced into the theatre. Directors make more of the echoing silences of large spaces, while contemplation and awe are encouraged – at least in certain, more serious, productions on the subsidised stage. Meanwhile, much of what's left of contemporary Christianity seems to have forsaken the same sense of awe and reverence in favour of light-filled modern halls, with barely a nod to traditional religious architecture. Over the course of the last week I happened to visit BAC, Tate Modern and Shunt Vaults. All are essentially found-spaces and all are evocative of particular moments in Christian architecture. Tate Modern, a Stalinist spin on medieval gothic; Shunt, with its high vaulted ceilings and long main space, edging toward the real thing; while the BAC's Grand Hall, now used by the venue for its scratch performances, was purpose built for late-Victorian, Salvation Army-style mass worship. Granted the work presented in each varies – Shunt last week had performers dressed as various animals fighting in cages, which I don't remember ever being incorporated into an act of worship. However, there was also, briefly, a moment of gorgeous choral singing by The Roundhouse Experimental Choir and the sheer churchliness of the space was suddenly, powerfully revealed. And this is precisely the point.

Some of the most successful avant garde work seems to be aiming to recapture this sense of the austere for a secular audience. Consider Franko B performing I Miss You! at the Tate Modern – in the midst of this cultural cathedral, a naked figure bleeds slowly, dripping on to a white cloth. Even taking into account its secular intent, the resonances don't need spelling out.

It is fascinating that while theatre and performance have a long history of challenging the teachings of organised religion, the spaces and resonances that they are now adopting seem to owe so much to its history.